Static and Dynamic Analysis of Multi-Story Buildings, Including P-Delta Effects

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Abstract
The P-Delta phenomenon is an area of concern to structural engineers. Traditional methods for incorporating P-Delta effects in analysis are based on iterative techniques. These techniques are time-consuming and are in general used for static analysis only. For building structures, the mass, which causes the P-Delta effect, is constant irrespective of the lateral loads and displacements. This information is used to linearize the P-Delta effect for buildings and solve the problem “exactly”, satisfying equilibrium in the deformed position, without iterations. An algorithm is developed that incorporates the P-Delta effects into the basic formulation of the structural stiffness matrix as a geometric stiffness correction. This procedure can be used for both static and dynamic analysis and will account for the lengthening of the structural time periods and changes in mode shapes due to P-Delta effects. The algorithm can be directly incorporated into building analysis programs.

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